A quick and dirty smoothing method is to replace each point by the average of itself and its two neighbours.

Yes, in fact that's the (degenerate case) Savitzky-Golay filter with N=0 {linear polynomial fit}, M=1 {window width = 1 point to the left and 1 point to the right of the fitted point}. Of course, selecting N=0 squanders all of the power of the S-G approach, which exactly matches the first N moments of the data.

I found a pretty nice paper by Shafer, 2nd author of the famous Oppenheim & Shafer DSP textbook which demystifies the S-G filter, by analyzing it in the frequency domain. Savitzky and Golay, chemists by profession, analyzed it only in the time domain. Nevertheless the fact that a couple of chemists devised an extremely useful FIR digital filter in 1964, is quite an achievement. As the jonsson.eu website says,

Quote:

The Savitzky—Golay smoothing filter was originally presented in 1964 by Abraham Savitzky [3] and Marcel J. E. Golay [4] in their paper Smoothing and Differentiation of Data by Simplified Least Squares Procedures, Anal. Chem., 36, 1627-1639 (1964) [2]. (Publicly available at Smoothing and Differentiation of Data by Simplified Least Squares Procedures. - Analytical Chemistry (ACS Publications).) Being chemists and physicists, at the time of publishing associated with the Perkin-Elmer Corporation (still today a reputable manufacturer of equipment for spectroscopy), they found themselves often encountering noisy spectra where simple noise-reduction techniques, such as running averages, simply were not good enough for extracting well-determined characteristica of spectral peaks. In particular, any running averaging tend to flatten and widening peaks in a spectrum, and as the peak width is an important parameter when determining relaxation times in molecular systems, such noise-reduction techniques are clearly non-desirable.

Eventually I decided that for the application I had in mind, presenting the raw data with visible DSO grunge was the best option. It throbs with the imperfect reality you see at the test bench. An example figure is below.